Method and apparatus for identifying assist feature placement problems

ABSTRACT

One embodiment of the present invention provides a system that identifies an area in a mask layout which is likely to cause manufacturing problems due to a missing or an improperly placed assist feature. During operation, the system receives an uncorrected or corrected mask layout. The system then dissects the mask layout into segments. Next, the system identifies a problem area associated with a segment using a process-sensitivity model which can be represented by a multidimensional function that captures process-sensitivity information. Note that identifying the problem area allows a new assist feature to be added or an existing assist feature to be adjusted, thereby improving the wafer manufacturability. Moreover, using the process-sensitivity model reduces the computational time required to identify the problem area.

RELATED APPLICATION

This application is a continuation-in-part of, and hereby claimspriority under 35 U.S.C. § 120 to, U.S. patent application Ser. No.11/083,656, entitled, “METHOD AND APPARATUS FOR IDENTIFYING AMANUFACTURING PROBLEM AREA IN A LAYOUT USING A GRADIENT-MAGNITUDE OF APROCESS-SENSITIVITY MODEL,” by inventors Lawrence S. Melvin III, JamesP. Shiely, and Qiliang Yan filed on 17^(th) Mar. 2005 (Attorney DocketNo. SNPS-0649).

BACKGROUND

1. Field of the Invention

The present invention is related to integrated circuit fabrication. Morespecifically, the present invention is related to a method and apparatusfor identifying assist feature placement problems.

2. Related Art

Semiconductor manufacturing technologies typically include a number ofprocesses which involve complex physical and chemical interactions.Since it is almost impossible to perfectly control these complexphysical and chemical interactions, these processes typically haveprocess variations that can cause the characteristics of the actualintegrated circuit to be different from the desired characteristics. Ifthis difference is too large, it can lead to manufacturing problemswhich can reduce the yield and/or reduce the performance of theintegrated circuit.

Consequently, to be economically viable, a semiconductor manufacturingprocess has to be robust with respect to process variations, i.e., itmust be able to tolerate a large enough range of process variations. (Wedescribe the present invention in the context of “depth of focus,” whichusually refers to process variations in photolithography. But, it willbe apparent to one skilled in the art that the present invention can bereadily applied to include other manufacturing process variations, suchas, dose variation, resist thickness variations, etch variations, anddoping variations.)

Note that improving the depth of focus directly results in cost savings.This is because it can substantially increase the throughput by reducingthe amount of time spent on inspection, servicing, and maintenance ofthe equipment. In addition, the actual process conditions encounteredduring manufacturing may vary due to a variety of reasons. For example,topographical variations on the wafer can occur due to imperfections inthe chemical-mechanical polishing process step. As a result, improvingthe depth of focus can increase the yield for chips that aremanufactured in the presence of these process variations.

Depth of focus can be improved by using assist features. Note thatassist features can be printing (e.g., super-resolution assist features)or non-printing (e.g., sub-resolution assist features). In either case,assist features are meant to improve the depth of focus of the patternson the mask layout intended to be printed on the wafer.

Unfortunately, using assist features to improve depth of focus can bevery challenging, especially at deep submicron dimensions. Processengineers typically create sophisticated rule tables that specify theshape and placement of assist features from empirical wafer data.Unfortunately, assist feature rule tables can result in missed orsub-optimal placement of assist features. Furthermore, at deep submicrondimensions, assist feature rule tables can be extremely large andunwieldy. Moreover, assist feature rule tables can be overly restrictivewhich can prevent designers from being able to achieve the best deviceperformance.

Hence, what is needed is a method and an apparatus to identify assistfeature placement problems so that they can be corrected, therebyimproving the manufacturability of the mask layout.

SUMMARY

One embodiment of the present invention provides a system thatidentifies an area in a mask layout which is likely to causemanufacturing problems due to a missing or an improperly placed assistfeature. During operation, the system receives an uncorrected orcorrected mask layout. The system then dissects the mask layout intosegments. Next, the system identifies a problem area associated with asegment using a process-sensitivity model which can be represented by amultidimensional function that captures process-sensitivity information.Note that identifying the problem area allows a new assist feature to beadded or an existing assist feature to be adjusted, thereby improvingthe wafer manufacturability. Moreover, using the process-sensitivitymodel reduces the computational time required to identify the problemarea.

In a variation on this embodiment, the system computes theprocess-sensitivity model by: creating an on-target process model thatmodels a semiconductor manufacturing process under nominal processconditions; creating one or more off-target process models that modelthe semiconductor manufacturing process under one or more processconditions that are different from nominal process conditions; andcomputing the process-sensitivity model using the on-target processmodel and the one or more off-target process models. Specifically, thesystem can compute the process-sensitivity model by computing a linearcombination of the on-target process model and the one or moreoff-target process models. Furthermore, the semiconductor manufacturingprocess can include: photolithography, etch, chemical-mechanicalpolishing (CMP), trench fill, or reticle manufacture.

In a variation on this embodiment, the system identifies the problemarea associated with the segment by first computing a problem-indicatorby convolving the process-sensitivity model with a multidimensionalfunction that represents the mask layout. Next, the system compares thevalue of the problem-indicator with a threshold to identify the problemarea associated with the segment.

In a further variation on this embodiment, the system determines thethreshold by first determining a segment-type of the segment based onthe feature geometry in the proximity of the segment. The system thenselects the threshold based on the segment-type. Note that using anappropriate threshold that is based on the segment-type allows themethod to accurately determine the type and the severity of the problemarea.

In a variation on this embodiment, the system identifies the problemarea associated with the segment by first computing a gradient-magnitudeof the process-sensitivity model. The system then computes aproblem-indicator by convolving the gradient-magnitude of theprocess-sensitivity model with a multidimensional function thatrepresents the mask layout. Next, the system compares the value of theproblem-indicator with a threshold to identify the problem areaassociated with the segment.

BRIEF DESCRIPTION OF THE FIGURES

FIG. 1 illustrates various steps in the design and fabrication of anintegrated circuit in accordance with an embodiment of the presentinvention.

FIG. 2 illustrates assist feature placement in a mask layout inaccordance with an embodiment of the present invention.

FIG. 3 illustrates assist feature placement using a rule-basedmethodology in accordance with an embodiment of the present invention.

FIG. 4 presents a flowchart that illustrates a process for identifying aproblem area in accordance with an embodiment of the present invention.

FIG. 5A illustrates a plot of a 2-D function that represents anon-target process model in accordance with an embodiment of the presentinvention.

FIG. 5B illustrates a plot of a 2-D function that represents anoff-target process model in accordance with an embodiment of the presentinvention.

FIG. 5C illustrates a plot of a process-sensitivity model in accordancewith an embodiment of the present invention.

FIG. 6 illustrates how the problem-indicator can be computed byintegrating the aerial-image intensity in accordance with an embodimentof the present invention.

FIG. 7A illustrates how a segment-type can be determined based on thefeature geometry in the proximity of a segment in accordance with oneembodiment of the present invention.

FIG. 7B illustrates a variety of feature geometries that can be used todetermine a segment-type in accordance with an embodiment of the presentinvention.

FIG. 8A and FIG. 8B illustrate how a gradient-magnitude of aprocess-sensitivity model can be used to identify an area in a masklayout which is likely to cause manufacturing problems due to missing orimproperly placed assist features in accordance with an embodiment ofthe present invention.

DETAILED DESCRIPTION

Integrated Circuit Design and Fabrication

FIG. 1 illustrates various steps in the design and fabrication of anintegrated circuit in accordance with an embodiment of the presentinvention. The process starts with a product idea (step 100). Next, theproduct idea is realized using an integrated circuit, which is designedusing Electronic Design Automation (EDA) software (step 110). Once thecircuit design is finalized, it is taped-out (step 140). After tape-out,the process goes through fabrication (step 150), packaging, and assembly(step 160). The process eventually culminates with the production ofchips (step 170).

The EDA software design step 110, in turn, includes a number ofsub-steps, namely, system design (step 112), logic design and functionverification (step 114), synthesis and design for test (step 116),design planning (step 118), netlist verification (step 120), physicalimplementation (step 122), analysis and extraction (step 124), physicalverification (step 126), resolution enhancement (step 128), and maskdata preparation (step 130).

The present invention can be used during one or more of the abovedescribed steps. Specifically, the SiVL® or the AFGen® product fromSynopsys, Inc. can be suitably modified to use the present invention toidentify problem areas in a mask layout.

Process Variations

Semiconductor manufacturing technologies typically include a number ofprocesses which involve complex physical and chemical interactions.Since it is almost impossible to perfectly control these complexphysical and chemical interactions, these processes typically haveprocess variations that can cause the characteristics of the actualintegrated circuit to be different from the desired characteristics. Ifthis difference is too large, it can lead to manufacturing problemswhich can reduce the yield and/or reduce the performance of theintegrated circuit.

Process variations can arise due to a variety of reasons. For example,in photolithography, variations in the rotation speed of the spindle cancause the resist thickness to vary, which can cause variations in thereflectivity, which, in turn, can cause unwanted changes to thepattern's image. Similarly, bake plates—which are used to drive thesolvents out of the wafer and form the pattern in photoresist—can havehot or cold spots, which can cause variations in the critical dimension(CD). Likewise, the chuck that holds the wafer during photo exposure cancontain microparticles which create “hills” on the wafer's surface thatcan cause defocusing during lithography. Note that defocusing can alsooccur because the chuck is out of level, or the lens has aberrations, orthe wafer is not completely flat, amongst other reasons.

It is helpful to classify process variations into two types: random andsystematic. (Note that the term “depth of focus” is often used as acatch-all term to describe the amount of process margin available tocompensate for random process variations.) Random process variations arethose process variations that are not presently being modeled using ananalytical model. On the other hand, systematic process variations arethose process variations that are typically modeled using analyticalmodels. For example, spindle speed variation is typically classified asa random process variation, while pattern corner rounding has beencompensated for in a systematic manner. Note that, researchers arecontinually trying to convert random process variations into systematicprocess variations by creating new analytical models that model randomprocess variations. Once a random process variation is understood tobecome a systematic process variation, the systematic variation cangenerally be compensated for during OPC.

Manufacturing Problems

To be economically viable, a semiconductor manufacturing process has tobe robust with respect to process variations, i.e., it must be able totolerate a large enough range of process variations. Note that,improving the robustness (or depth of focus) of a process directlyresults in cost savings. This is because improving depth of focusreduces the amount of time spent on inspection, servicing, andmaintenance of the equipment, thereby increasing the number of wafersthat are run. Furthermore, improving the depth of focus can increase theyield. Due to these reasons, increasing depth of focus can substantiallyincrease profits.

Moreover, the importance of improving depth of focus increases as amanufacturing process shifts to smaller dimensions because the inherentdepth of focus in these processes becomes rapidly smaller. Specifically,at deep submicron dimensions, even a small improvement in the depth offocus can save millions of dollars in manufacturing costs.

Assist Features

Assist features are often used for improving depth of focus duringsemiconductor manufacturing. In particular, sub-resolution assistfeatures (SRAFs) have been especially effective when applied to gatestructures and other one-dimensional features. (For the sake of clarity,the present invention has been described in the context ofsub-resolution assist features. But, it will be apparent to one skilledin the art that the present invention can be readily applied to otherkinds of assist features, such as super-resolution assist features. Inthe remainder of the instant application, unless otherwise stated, theterm “assist feature” will refer to a sub-resolution assist feature.)

FIG. 2 illustrates assist feature placement in a mask layout inaccordance with an embodiment of the present invention.

Lines 202 and 204 are part of a mask layout. Note that line 204 containscomplex feature 206. Assist feature placement is more challenging when alayout contains complex features. For example, due to the complexfeature 206, we may need to place two assist features 208 and 210 thatare staggered, instead of just one assist feature. A layout that hasmultiple lines with varying pitches is another example of a complexlayout.

Present methods for placing assist features use a rule-based methodologywhere the assist feature placement is dictated by combinations offeature width and spacing parameters.

FIG. 3 illustrates assist feature placement using a rule-basedmethodology in accordance with an embodiment of the present invention.

Lines 302, 304, 306, and 308 are part of a mask layout. In a rule-basedapproach, assist feature (AF) 318 placement can depend on a variety offactors which are organized in the form of a rule table. For example,the AF distance 320 can be a determined based on a rule table thatincludes a variety of factors, such as, the critical dimension (CD) 310,space 312, length 314, and gap 316.

Unfortunately, design rule tables can result in missed or sub-optimalplacement of assist features. Furthermore, for large and complex layoutsthe rule table can become extremely large and unwieldy. Moreover, designrule tables can be overly restrictive which can prevent designers frombeing able to achieve the best device performance.

Identifying Assist Feature Placement Problems

One of the primary goals of semiconductor manufacturing is to, in onemeasurement, get all the process variation information at a point on amask layout. If we achieve this, we can identify and correctmanufacturing problem areas due to missing or incorrectly placed assistfeatures, thereby improving the manufacturability of the mask layout.For example, if we know that a line-end is highly sensitive to processvariations and is likely to pull back 40 nm during manufacturing, thedesigner can use this information to add or adjust an assist feature tofix the manufacturing problem.

Furthermore, it is very important that we identify these problem areaswithout using a substantial amount of computation time. Note thatproblem areas can be identified by simulating various process conditionsand by comparing the resulting patterns to determine areas that cancause manufacturability problems. Unfortunately, this approach canrequire a substantial amount of computational time because it involvesrunning multiple complex simulation models.

Instead, what is needed is a process that can quickly tell us whether anassist feature is going to improve the stability of a structure within aworkable process window. (Note that determining whether a structure isstable or not depends on the type of the layer. For example, in a metallayer, significant CD variations may be acceptable as long as they donot cause a short or an open in the circuit. In contrast, in apolysilicon layer, even very small CD variations may be unacceptable.)

One embodiment of the present invention provides a system foridentifying an area in a mask layout which is likely to causemanufacturing problems due to missing or improperly placed assistfeatures. Specifically, in one embodiment of the present invention, thesystem uses a gradient-magnitude of a “process-sensitivity model” (whichcan be represented using a multidimensional function that capturesprocess-sensitivity information) to query a pattern and generate aproblem indicator that indicates the amount of process variation that isexpected to occur at any point on mask layout. Based on the amount ofprocess variation, a designer can decide whether it is likely to causeproblems during manufacturing and take appropriate counter measures,such as adding or adjusting an assist feature.

Furthermore, in one embodiment of the present invention, the system usesthe computed problem indicator to generate a contour. Specifically, thecontour can be used to indicate the type and severity of the assistfeature placement problem. Note that generating a contour can be veryuseful because it interprets the process variation data and visuallyidentifies the problem areas to the user. Moreover the contour can bedisplayed using a standard optical intensity viewing tool, such as theICWorkbench™ tool from Synopsys.

Note that a key advantage is that the process can captureprocess-sensitivity information in a single multidimensional function.(Note that, to improve computational efficiency, a multidimensionalfunction is often represented using a linear combination of a set oforthogonal functions, which are typically called basis functions. But,from a mathematical standpoint, the process-sensitivity model can stillbe viewed as a single multidimensional function.) Furthermore, thisallows the system to directly identify the problem area. Specifically,the system can quickly compute a problem-indicator by simply convolvingthe gradient-magnitude of the process-sensitivity model with anothermultidimensional function that represents the mask layout. The systemcan then compare the problem-indicator with a threshold to identify amanufacturing problem area, thereby substantially reducing the amount ofcomputational time required to identify the manufacturing problem area.

Using a Process-Sensitivity model to Identify Assist Feature PlacementProblems

FIG. 4 presents a flowchart that illustrates a process for identifying aproblem area in accordance with an embodiment of the present invention.

The process typically begins by receiving a mask layout which cancontain assist features (step 402).

The system then dissects the mask layout into a number of segments (step404). Note that a segment can be any arbitrary portion of a polygonedge.

Next, the system identifies a problem area associated with a segmentusing a process-sensitivity model which can be represented by amultidimensional function that captures process-sensitivity information.Specifically, in one embodiment, the system identifies a problem areaassociated with a segment using a gradient-magnitude of theprocess-sensitivity model.

Note that, the system can compute the process-sensitivity model by firstcreating an on-target process model that models a semiconductormanufacturing process under nominal process conditions. Furthermore,note that the semiconductor processing technology can includephotolithography, etch, chemical-mechanical polishing (CMP), trenchfill, and/or other technologies and combinations of the foregoing.

Next, the system can create one or more off-target process models thatmodel the semiconductor manufacturing process under one or more processconditions that are different from nominal process conditions.

Specifically, an on-target (or off-target) process model can berepresented by a multidimensional function. Moreover, an on-target (oroff-target) process model can be represented using a set of basisfunctions. Furthermore, in one embodiment, creating an on-target processmodel involves fitting an analytical model to process data for thesemiconductor manufacturing process under nominal process conditions.Likewise, creating the one or more off-target process models can involvefitting an analytical model to process data for the semiconductormanufacturing process under process conditions that are different fromnominal process conditions. Additionally, in one embodiment, the one ormore off-target process models can be created by analytically perturbingthe on-target process model.

FIG. 5A illustrates a plot of a 2-D function that represents anon-target process model in accordance with an embodiment of the presentinvention.

FIG. 5B illustrates a plot of a 2-D function that represents anoff-target process model in accordance with an embodiment of the presentinvention.

FIG. 5C illustrates a plot of a process-sensitivity model in accordancewith an embodiment of the present invention.

Note that the 2-D functions illustrated in FIG. 5A and FIG. 5B representthe on-target and the off-target process models, respectively, in thespatial frequency domain. Furthermore, in FIG. 5A, FIG. 5B, and FIG. 5C,the X and Y axes identify a spatial-frequency component (in units ofradians per micron), whereas the Z axis indicates the magnitude of aspecific spatial-frequency component. These process models can also berepresented in other domains, such as the space domain. Additionally,these process models can also be represented in other coordinates, suchas polar coordinates.

In one embodiment, the system computes the process-sensitivity model bycomputing a linear combination of the on-target process model and theone or more off-target process models. Note that the process-sensitivitymodel models the pattern features that are lost during defocus.

Specifically, consider the optical lithography case. Let P_(t) representan on-target process model, i.e., let P_(t) model the opticallithography process when it is in focus. Furthermore, let P_(d)represent an off-target process model, e.g., let P_(d) model the opticallithography process when it is defocused. Now, the process-sensitivitymodel, F_(p) can be computed as follows: F_(p)=(P_(t)−P_(d))/ΔP_(d),where ΔP_(d) is the focus offset (in units of length).

Note that in the above example, we only considered a single off-targetprocess model. But, we can have two or more off-target process models.In general, the process-sensitivity model, F_(p), can be computed asfollows:${F_{p} = {\frac{1}{n}\left( {{\frac{1}{\Delta\quad P_{1}}\left( {P_{t} - P_{1}} \right)} + {\frac{1}{\Delta\quad P_{2}}\left( {P_{t} - P_{2}} \right)} + \ldots + {\frac{1}{\Delta\quad P_{n}}\left( {P_{t} - P_{n}} \right)}} \right)}},$where P_(1 . . . n) are off-target process models that model arbitrary(e.g., non-optimal) process conditions, P_(t) is the on-target processmodel that models a nominal (e.g., optimal) process condition, andΔP_(1 . . . n), are the respective changes in the process conditionsbetween the nominal process condition and the arbitrary (1 . . . n)process conditions.

For example, let P_(t) model the optical lithography process when it isin focus. Furthermore, let P_(dn) model the optical lithography processwhen it is negatively defocused, i.e., the distance between the lens andthe wafer is less than the on-target distance. Additionally, let P_(dp)model the optical lithography process when it is positively defocused,i.e., the distance between the lens and the wafer is larger than theon-target distance. Now, the process-sensitivity model, F_(p), can becomputed as follows:${F_{p} = {\frac{1}{2}\left( {\frac{\left( {P_{0} - P_{dn}} \right)}{\Delta\quad P_{dn}} + \frac{\left( {P_{0} - P_{dn}} \right)}{\Delta\quad P_{dp}}} \right)}},$where ΔP_(dn) and ΔP_(dp) are the negative and positive focus offsets(in units of length).

Note that, (P_(t)−P_(dn))/ΔP_(dn) and (P_(t)−P_(dp))/ΔP_(dp) model thepattern features that are lost during negative and positive defocusing,respectively. In the above example, we compute the process-sensitivitymodel, F_(p), by adding (P_(t)−P_(dn))/ΔP_(dn) and(P_(t)−P_(dp))/ΔP_(dp), and by dividing by 2 to normalize theprocess-sensitivity model. (Note that normalization is not necessary forthe invention to work.)

In one embodiment, the system then computes a gradient-magnitude of theprocess-sensitivity model. Note that the term “gradient-magnitude” canbroadly refer to a rate of change of the process-sensitivity model.Furthermore, it will also be apparent that the gradient-magnitude forthe process-sensitivity model can be computed using a variety ofmathematical formulae. Specifically, in one embodiment of the presentinvention, the system computes the gradient-magnitude of theprocess-sensitivity model, G_(p), as follows:${G_{p} = {{{\nabla\frac{1}{n}}\left( {{\frac{1}{\Delta\quad P_{1}}\left( {P_{t} - P_{1}} \right)} + {\frac{1}{\Delta\quad P_{2}}\left( {P_{t} - P_{2}} \right)} + \ldots + {\frac{1}{\Delta\quad P_{n}}\left( {P_{t} - P_{n}} \right)}} \right)}}},$where P_(1 . . . n) are off-target process models that model arbitrary(e.g., non-optimal) process conditions, P_(t) is the on-target processmodel that models a nominal (e.g., optimal) process condition, andΔP_(1 . . . n) are the respective changes in the process conditionsbetween the nominal process condition and the arbitrary (1 . . . n)process conditions.

Continuing with the flowchart of FIG. 4, the system computes aproblem-indicator by convolving the gradient-magnitude of theprocess-sensitivity model with a multidimensional function thatrepresents the mask layout (step 406). In one embodiment, the systemcomputes the problem-indicator at an evaluation point in the proximityof a segment. Moreover, the system can store the value of theproblem-indicator in a database so that the value of theproblem-indicator at a location in the mask layout can be found byquerying the database.

In another embodiment, the system can compute the problem-indicator byconvolving the process-sensitivity model with a multidimensionalfunction that represents the mask layout.

In yet another embodiment, the problem-indicator can be computed at anevaluation point by first integrating the aerial-image intensity over anarea around the evaluation point. The system can then compute theproblem-indicator by taking the partial derivative of the integral withrespect to the defocus offset.

FIG. 6 illustrates how the problem-indicator can be computed byintegrating the aerial-image intensity in accordance with one embodimentof the present invention.

Let I(r,θ) represent the aerial-image intensity in polar coordinates,where r is the radial distance between evaluation point 602 andelemental area r·dr·dθ, and θ is the angle between reference line 608and line 610 which passes through evaluation point 602 and elementalarea r·dr·dθ.

The system can compute the surface integral, P, of the aerial-image overarea A as follows: P = ∫∫_(A)I(r, θ) ⋅ r ⋅ 𝕕r ⋅ 𝕕θ.

Next, the system can compute the problem-indicator at the evaluationpoint by computing the partial derivative of P with respect to thedefocus offset.

Continuing with the flowchart in FIG. 4, the system then compares thevalue of the problem-indicator with a threshold to identify a problemarea associated with the segment. Specifically, in one embodiment, thesystem determines a segment-type of the segment based on the featuregeometry in the proximity of the segment (step 408).

FIG. 7A illustrates how a segment-type can be determined based on thefeature geometry in the proximity of a segment in accordance with oneembodiment of the present invention.

Pattern 702 can be dissected into segments 706, 708, 710, 712, and 714.(Note that, usually each edge of a pattern is dissected into one or moresegments. But, in FIG. 7A, for the sake of clarity, we only dissect oneedge of pattern 702.)

Note that the system can dissect a mask layout into segments based onhow features (or patterns) are positioned relative to one another. Forexample, in the absence of assist feature (AF) 704, the system couldhave dissected pattern 702 into only three segments: 706, 714, and asingle segment that combines 708, 710, and 712.

The system can then determine a segment-type for a segment based on thefeature geometry in the proximity of the segment. For example, segments706 and 714 can be classified as 2-D region segments, segments 708 and712 can be classified as 1-D run segments, and segment 710 can beclassified as an AF transition segment.

Note that the term “feature geometry” can refer to the shape and size ofone or more features associated with a segment as well as the positionof the segment relative to other features or patterns in the masklayout.

Note that the segment-types disclosed in the present application are notintended to be exhaustive or to limit the present invention.Accordingly, many variations of feature geometries and associatedsegment-types will be readily apparent.

Specifically, FIG. 7B illustrates a variety of feature geometries thatcan be used to determine a segment-type in accordance with an embodimentof the present invention.

Continuing with the flowchart of FIG. 4, the system selects the problemthreshold based on the segment-type (step 410). Note that using anappropriate threshold that is based on the segment-type allows themethod to accurately determine the type and the severity of the problemarea.

The system then identifies the problem area by comparing theproblem-indicator with the problem threshold (step 412).

FIG. 8A and FIG. 8B illustrate how a gradient-magnitude of aprocess-sensitivity model can be used to identify an area in a masklayout which is likely to cause manufacturing problems due to missing orimproperly placed assist features in accordance with an embodiment ofthe present invention.

The mask layout shown in FIG. 8A includes a number of uncorrectedpatterns, such as patterns 802, 804, and 806. (Note that embodiments ofthe present invention can be used to identify manufacturing problemareas in an uncorrected, partially corrected, or completely correctedmask layout.)

The system can use a gradient-magnitude of a process-sensitivity modelto identify manufacturing problem areas, such as, problem areas 808,810, and 816, which are caused by missing or improperly placed assistfeatures.

Note that a process engineer can use this information to add or adjustassist features, thereby improving the manufacturability of the masklayout.

Specifically, FIG. 8B illustrates the mask layout after adding andadjusting assist features at various locations. For example, newly addedassist features 812 and 814 correct problem areas 808 and 810,respectively.

Note that, adding and adjusting various assist features to the masklayout shown in FIG. 8A did not correct problem area 816. Hence, adesigner may need to add or adjust assist features in the proximity ofproblem area 816 to correct the problem to improve the manufacturabilityof the layout.

In one embodiment, the system can display these problem areas using astandard optical intensity viewing tool. Note that the system can use anumber of visual cues to indicate the type and severity of themanufacturing problem. For example, the system can use a specific colorto indicate the type of the manufacturing problem. Moreover, the systemcan use the width of the marker that specifies the location of theproblem area to indicate the severity of the manufacturing problem.

CONCLUSION

The data structures and code described in the foregoing description aretypically stored on a computer-readable storage medium, which may be anydevice or medium that can store code and/or data for use by a computersystem. This includes, but is not limited to, magnetic and opticalstorage devices such as disk drives, magnetic tape, CDs (compact discs)and DVDs (digital versatile discs or digital video discs), and computerinstruction signals embodied in a transmission medium (with or without acarrier wave upon which the signals are modulated). For example, thetransmission medium may include a communications network, such as theInternet.

Furthermore, the foregoing descriptions of embodiments of the presentinvention have been presented only for purposes of illustration anddescription. They are not intended to be exhaustive or to limit thepresent invention to the forms disclosed. Accordingly, manymodifications and variations will be readily apparent to practitionersskilled in the art. Additionally, the above disclosure is not intendedto limit the present invention. The scope of the present invention isdefined by the appended claims.

1. A method for identifying an area in an uncorrected or corrected masklayout which is likely to cause manufacturing problems due to a missingor an improperly placed assist feature, the method comprising: receivinga mask layout; dissecting the mask layout into segments; and identifyinga problem area associated with a segment using a process-sensitivitymodel which can be represented by a multidimensional function thatcaptures process-sensitivity information; wherein identifying theproblem area allows a new assist feature to be added or an existingassist feature to be adjusted, thereby improving the wafermanufacturability of the mask layout; wherein using theprocess-sensitivity model reduces the computational time required toidentify the problem area.
 2. The method of claim 1, wherein theprocess-sensitivity model can be computed by, creating an on-targetprocess model that models a semiconductor manufacturing process undernominal process conditions; creating one or more off-target processmodels that model the semiconductor manufacturing process under one ormore process conditions that are different from nominal processconditions; and computing the process-sensitivity model using theon-target process model and the one or more off-target process models.3. The method of claim 2, wherein computing the process-sensitivitymodel involves computing a linear combination of the on-target processmodel and the one or more off-target process models.
 4. The method ofclaim 1, wherein identifying the problem area associated with thesegment involves: computing a gradient-magnitude of theprocess-sensitivity model; computing a problem-indicator by convolvingthe gradient-magnitude of the process-sensitivity model with amultidimensional function that represents the mask layout; comparing thevalue of the problem-indicator with a threshold to identify the problemarea associated with the segment.
 5. The method of claim 4, wherein thethreshold is determined by, determining a segment-type of the segmentbased on the feature geometry in the proximity of the segment; andselecting the threshold based on the segment-type, wherein using anappropriate threshold based on the segment-type allows the method toaccurately determine the type and the severity of the problem area. 6.The method of claim 1, wherein identifying the problem area associatedwith the segment involves: computing a problem-indicator by convolvingthe process-sensitivity model with a multidimensional function thatrepresents the mask layout; determining a segment-type of the segmentbased on the feature geometry in the proximity of the segment; selectinga threshold based on the segment-type, wherein using an appropriatethreshold based on the segment-type allows the method to accuratelydetermine the type and the severity of the problem area; and comparingthe value of the problem-indicator with the threshold to identify theproblem area associated with the segment.
 7. The method of claim 1,wherein identifying the problem area associated with the segmentinvolves: computing an integral of an aerial-image intensity functionover a surface area in the proximity of the segment; computing a partialderivative of the integral of the aerial-image intensity function;determining a segment-type of the segment based on the feature geometryin the proximity of the segment; selecting a threshold based on thesegment-type, wherein using an appropriate threshold based on thesegment-type allows the method to accurately determine the type and theseverity of the problem area; and comparing the value of the partialderivative with the threshold to identify the problem area associatedwith the segment.
 8. The method of claim 2, wherein the semiconductormanufacturing process can include: photolithography; etch;chemical-mechanical polishing (CMP); trench fill; or reticlemanufacture.
 9. A computer-readable storage medium storing instructionsthat when executed by a computer cause the computer to perform a methodfor identifying an area in an uncorrected or corrected mask layout whichis likely to cause manufacturing problems due to a missing or animproperly placed assist feature, the method comprising: receiving amask layout; dissecting the mask layout into segments; and identifying aproblem area associated with a segment using a process-sensitivity modelwhich can be represented by a multidimensional function that capturesprocess-sensitivity information; wherein identifying the problem areaallows a new assist feature to be added or an existing assist feature tobe adjusted, thereby improving the wafer manufacturability of the masklayout; wherein using the process-sensitivity model reduces thecomputational time required to identify the problem area.
 10. Thecomputer-readable storage medium of claim 9, wherein theprocess-sensitivity model can be computed by, creating an on-targetprocess model that models a semiconductor manufacturing process undernominal process conditions; creating one or more off-target processmodels that model the semiconductor manufacturing process under one ormore process conditions that are different from nominal processconditions; and computing the process-sensitivity model using theon-target process model and the one or more off-target process models.11. The computer-readable storage medium of claim 10, wherein computingthe process-sensitivity model involves computing a linear combination ofthe on-target process model and the one or more off-target processmodels.
 12. The computer-readable storage medium of claim 9, whereinidentifying the problem area associated with the segment involves:computing a gradient-magnitude of the process-sensitivity model;computing a problem-indicator by convolving the gradient-magnitude ofthe process-sensitivity model with a multidimensional function thatrepresents the mask layout; comparing the value of the problem-indicatorwith a threshold to identify the problem area associated with thesegment.
 13. The computer-readable storage medium of claim 12, whereinthe threshold is determined by, determining a segment-type of thesegment based on the feature geometry in the proximity of the segment;and selecting the threshold based on the segment-type, wherein using anappropriate threshold based on the segment-type allows the method toaccurately determine the type and the severity of the problem area. 14.The computer-readable storage medium of claim 9, wherein identifying theproblem area associated with the segment involves: computing aproblem-indicator by convolving the process-sensitivity model with amultidimensional function that represents the mask layout; determining asegment-type of the segment based on the feature geometry in theproximity of the segment; selecting a threshold based on thesegment-type, wherein using an appropriate threshold based on thesegment-type allows the method to accurately determine the type and theseverity of the problem area; and comparing the value of theproblem-indicator with the threshold to identify the problem areaassociated with the segment.
 15. The computer-readable storage medium ofclaim 9, wherein identifying the problem area associated with thesegment involves: computing an integral of an aerial-image intensityfunction over a surface area in the proximity of the segment; computinga partial derivative of the integral of the aerial-image intensityfunction; determining a segment-type of the segment based on the featuregeometry in the proximity of the segment; selecting a threshold based onthe segment-type, wherein using an appropriate threshold based on thesegment-type allows the method to accurately determine the type and theseverity of the problem area; and comparing the value of the partialderivative with the threshold to identify the problem area associatedwith the segment.
 16. The computer-readable storage medium of claim 10,wherein the semiconductor manufacturing process can include:photolithography; etch; chemical-mechanical polishing (CMP); trenchfill; or reticle manufacture.
 17. An apparatus for identifying an areain an uncorrected or corrected mask layout which is likely to causemanufacturing problems due to a missing or an improperly placed assistfeature, the apparatus comprising: a receiving mechanism configured toreceive a mask layout; a dissecting mechanism configured to dissect themask layout into segments; and an identifying mechanism configured toidentify a problem area associated with a segment using aprocess-sensitivity model which can be represented by a multidimensionalfunction that captures process-sensitivity information; whereinidentifying the problem area allows a new assist feature to be added oran existing assist feature to be adjusted, thereby improving the wafermanufacturability of the mask layout; wherein using theprocess-sensitivity model reduces the computational time required toidentify the problem area.
 18. The apparatus of claim 17, wherein theapparatus is configured to: create an on-target process model thatmodels a semiconductor manufacturing process under nominal processconditions; create one or more off-target process models that model thesemiconductor manufacturing process under one or more process conditionsthat are different from nominal process conditions; and compute theprocess-sensitivity model using the on-target process model and the oneor more off-target process models.
 19. The apparatus of claim 17,wherein the identifying mechanism is configured to: compute agradient-magnitude of the process-sensitivity model; compute aproblem-indicator by convolving the gradient-magnitude of theprocess-sensitivity model with a multidimensional function thatrepresents the mask layout; determine a segment-type of the segmentbased on the feature geometry in the proximity of the segment; select athreshold based on the segment-type, wherein using an appropriatethreshold based on the segment-type allows the method to accuratelydetermine the type and the severity of the problem area; and compare thevalue of the problem-indicator with the threshold to identify theproblem area associated with the segment.
 20. The apparatus of claim 17,wherein the identifying mechanism is configured to: compute aproblem-indicator by convolving the process-sensitivity model with amultidimensional function that represents the mask layout; determine asegment-type of the segment based on the feature geometry in theproximity of the segment; select a threshold based on the segment-type,wherein using an appropriate threshold based on the segment-type allowsthe method to accurately determine the type and the severity of theproblem area; and compare the value of the problem-indicator with thethreshold to identify the problem area associated with the segment.